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比利时vs摩洛哥足彩
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比利时vs摩洛哥足彩
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university of california san diego
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math 243, functional analysis seminar
dr. jitendra prakash
university of new orleans
constant-sized robust self-tests for states and measurements of unbounded dimension
abstract:
in quantum information, robust self-test is a desirable property for quantum devices through which one can certify the quantum-mechanical promises of the device based solely on classical statistics. we consider quantum correlations, $p_{n,x}$, arising from measuring a maximally entangled state using n measurements with two outcomes each, constructed from n projections that add up to xl. we show that the correlations $p_{n,x}$ robustly self-test the underlying states and measurements. to achieve this, we lift the group-theoretic gowers-hatami based approach for proving robust self-tests to a more natural algebraic framework. a key step is to obtain an analogue of the gowers-hatami theorem allowing to perturb an ``approximate'' representation of the relevant algebra to an exact one. for n = 4, the correlations $p_{n,x}$ self-test the maximally entangled state of every dimension as well as 2-outcome projective measurements of arbitrarily high rank.
hosts: david jekel and priyanga ganesan
january 31, 2023
11:00 am
zoom (email djekel@ucsd.edu for zoom info)
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